Theorem orim2d 790

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 788	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 710

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  791  orbi2d  792  pm2.82  814  stdcndcOLD  848  pm2.13dc  887  exmid1dc  4252  acexmidlemcase  5952  poxp  6331  fodjuomnilemdc  7261  omniwomnimkv  7284  exmidontriimlem1  7349  indpi  7475  suplocexprlemloc  7854  nneoor  9495  uzp1  9702  maxabslemlub  11593  xrmaxiflemlub  11634  nninfctlemfo  12436  exmidunben  12872  bj-nn0suc  16038  sbthomlem  16105